臺灣博碩士論文加值系統

要在合理時間內進行微米等級解析度的掃描時，核磁共振顯微技術的訊雜比一直是一個很大的限制。利用擴散現象增強訊號強度及解析度(Diffusion Enhancement of Signal and Resolution, DESIRE)的概念被提出後，訊雜比大約可以增加一個至三個數量級。在先前的研究中，模擬外加磁場的效應通常是使用疊代數值法計算，而擴散的效應則是利用有限微分法解Bloch-Torrey equation計算，這樣的模擬方法通常很耗時。在本實驗中，我們分別利用Shinnar-LeRoux演算法及基於旋積的擴散模擬方法來分別加速計算外加磁場及擴散對於磁振訊號的影響，可以節省大量運算時間，也讓二維DESIRE模擬可行。由模擬結果指出，我們可以使用射頻脈衝持續時間為零的飽和磁化向量代表持續時間不為零的情況在可接受合理誤差範圍內。我們也利用一維模擬結果預測在不同參數實驗中的有效解析度和訊號增益值，並找出最佳的參數值，在本實驗模擬結果指出Sinc3脈衝波形能同時兼顧良好的空間解析度及訊號增益值，對於總擴散時間為一秒時，施加100次Sinc3脈衝波形能得到最佳訊號增益值，也就是射頻脈衝的間隔為10 毫秒。由實驗結果中可得一維飽和剖繪圖及DESIRE影像也顯示出與模擬結果高度的相關性。對於在二維DESIRE影像中飽和一個圓柱體積來說，我們也提出梯度磁場系統需求的建議，並且指出除了梯度磁場強度之外，上升速率的硬體限制在二維實驗中也會有決定性的影響。

Within an advisable measurement time, the signal-to-noise ratio (SNR) is a major limitation of nuclear magnetic resonance (NMR) microscopy at the spatial resolution of micrometers level. The ‘‘Diffusion Enhancement of Signal and Resolution’’ (DESIRE) scheme provides potential signal enhancement about 1-3 order of magnitude enhancement. In the previous report, the calculations of external magnetic fields and diffusion propagation are simulated by iterative numerical optimization methods and finite-differential (FD) method of Bloch-Torrey equation, respectively. The disadvantage of these processes is time-consuming. In this work, the simulation of external magnetic fields is accelerated by Shinnar-LeRoux (SLR) algorithm and diffusion propagation is accelerated by convolution-based on diffusion simulation method. Thus, the time-cost of simulation can be saved, reducing especially for 2D DESIRE simulations. We can use the saturation magnetization profile with the pulse duration of zero to instead that of non-zero within acceptable error range. The 1D simulation results reveal the optimal parameters setting of restricted condition and predict the effective resolution and the enhancement of different parameters for experiments. The simulated results indicate the pulse waveform of Sinc3 has the both sufficient spatial resolution as well as enhancement in this study. As the total diffusion time is constant of 1 s, the optimal enhancement can be achieved using the pulse number of Sinc3 pulse of 100, namely a RF pulse interval of 10 ms. We also present the 1D saturation profiles and DESIRE images of experiments, and the enhancements of that have high degree agreement with simulated values. For saturating a cylinder volume of 2D DESIRE technique, the gradient system requirements are suggested using spiral gradient method. The simulated results reveal that the requirement of gradient slew rate is also a critical factor as the gradient strength.

List of Figures vii
List of Tables x
1 Introduction 1
2 Theory 3
2.1 Diffusion enhancement 3
2.2 Spatial resolution 4
2.3 Shinnar-Le Roux (SLR) algorithm 8
2.4 Random walk process 12
2.5 Molecular diffusion of NMR 14
2.6 K-space interpretation of small-tip excitation 15
3 Materials and methods 17
3.1 Bloch equation simulation 19
3.1.1 Matrix basics 19
3.1.2 Forward SLR transform 21
3.2 Diffusion simulation 22
3.2.1 Convolution-based method 22
3.2.2 Finite difference (FD) method 23
3.3 2D spiral gradient and RF pulse design 24
3.4 Experiments 29
3.4.1 1D DESIRE profiles 29
3.4.2 1D DESIRE images 30
4 Results 32
4.1 1D DESIRE simulations 32
4.1.1 Comparison of different pulse duration 32
4.1.2 Simulated magnetization profiles 36
4.1.3 The influences of the diffusion coefficient 40
4.1.4 The influences of the number of saturation pulses 43
4.1.5 The optimal parameters with relaxation 46
4.2 1D DESIRE experiments 47
4.2.1 Experimental magnetization profiles 47
4.2.2 Diffusion enhanced images of a plant stem 50
4.3 2D DESIRE simulations 51
4.3.1 Spiral gradients and RF pulse waveform 51
4.3.2 Simulated magnetization profiles and system requirements 54
5 Discussion 57
6 Conclusions 60
Appendix A 62
Bibliography 66

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